Time travel

I'm wondering whether anyone is familiar with the following argument regarding the impossibility of traveling into the past. I thought it up on my own, but I figure that I can't be the first. Any comments would be appreciated:

Traveling into the past violates first law of thermodynamics - the conservation of energy. Energy can’t be created, which would happen if you appeared in the past; energy can’t be destroyed, which would happen if you left the present for the past. For example, suppose a person travels to the past to meet one self. There are now 2 of them in one place. In other words, the energy of an entire person has been created.

This apparent contradiction might be explained by the following: all time, from beginning to end, is the same space and thus has a certain amount of energy, regardless of where a person travels in time. However, this explanation leads to another violation of the conservation of energy. Theoretically, a person could travel back in time repeatedly; for example, the person could travel back 1 year, meet his past self, then travel back 6 months, creating 3 of the same person. This implies that the person could have an infinite number of selves, as could anyone else. As a result, the universe could contain an infinite amount of energy. Since the universe has a finite amount of energy, an infinite number of selves couldn’t exist, so a person could not travel into the past.